1. Field of the Invention
This invention relates to convoluting two mutually scanned functions by multiplying Fourier series of the functions; and more particularly to multiplying terrain and antenna gain data at each range point for causing azimuth beamspreading in a simulated radar display.
2. Discussion of the Prior Art
FIG. 1 shows an airborne radar system 10 in operation. A receive-transmit antenna 12 mounted on aircraft 14 rotates or scans back and forth across a field-of-vision 16. A typical field of view extends 45.degree. on either side of the line of flight, and a typical scan rate about 40.degree. per second. Antenna 12 transmits directional radar pulses at a pulse rate (PRF) of typically 2000 pulses per second. A display CRT 18 mounted in aircraft 14 displays field-of-view 16 by generating a series of electron beam sweeps 20. Each sweep 20 extends from a display vertex at a distance from vertex 22 corresponding to the range of the object. The intensity of the display spot is a function of the reflectivity and distance of the object times the combined transmit-receive gain of antenna 12. A typical composite transmit-receive antenna gain pattern is shown at 24. Gain pattern 24 has a central main lobe 26 aligned with antenna bore site 27. Gain pattern 12 also has a secondary portion formed by major side lobes 28 of low gain and minor side lobes 30 of even less gain. Minor side lobes 30 provide such a minimal return pulse that they can effectively be ignored in training simulation of the FIG. 1 actual radar system. Main lobe 26 and major side lobes 28 define an instantaneous field-of-view 31 of typically from about one to about ten degrees within overall field-of-view 16. Each terrain object such as water tower 32, generates a display spot in display 18 for each electron beam sweep 20, because each transmit pulse from antenna 12 extends over the same instantaneous field-of-view 31 from which the return pulses are collected. The display spot brightness is negligible for sweeps 20 corresponding in position to minor side lobes 30, low for sweeps 20 corresponding in position to major side lobes 28, and brightest for sweeps 20 positionally corresponding to main lobe 26. As antenna 12 scans to the right, placing main lobe 26 into sequential positions A, B and C (shown in dashed lines), water tank 32 becomes positionally aligned with the high gain main lobe 26 and the water tank display spots become brighter due to the higher gain of antenna 12. At subsequent main lobe positions D, E and F, water tank 32 moves out of alignment with main lobe 26 and into the left-hand portion of major side lobe 28. The display bightness drops at positions D, E and F because of the lower side lobe gain of antenna 12.
Azimuth beamspread of water tank 32 in display 18 of the actual radar system 10 is caused by the thickness of main lobe 26 and by major side lobes 28 which generate a small but visible display spot in each side lobe sweep when antenna 12 is not directed at water tank 32. The water tank display spots have the same range on display 18, but occupy adjacent sweeps. The collective effect of the water tank display spots is a larger spot having a smeared appearance. The collective spot has a bright center portion formed by all of the sweeps within the beamwidth of main lobe 26. In addition, the collective spot has a left-hand and right-hand tail of progressively decreasing intensity caused by the progressively decreasing gain of right-hand and left-hand side lobes 28, respectively.
Heretofore, in radar simulation devices the azimuth beamspread effect was reproduced by retrieving data on R range points in each of the M sweeps within main lobe 26 and major side lobes 28. The data was retrieved point by point from a large data grid or map and arranged in an R bit.times. M bit memory. As antenna 12 scanned across field-of-view 16 a new lead sweep 34 was loaded into one end of the R.times. M memory and the expired trail sweep 36 was dumped out the other end. The R.times. M memory was updated for each transmit-return pulse or CRT sweep 20. The data in the R.times. M memory was pure or ideal terrain data without the azimuth beamspread smear or distortion. The azimuth beamspread smear was introduced by weighting and averaging technique described in U.S. patent application No. 3,919,535 entitled "Multiple Addend Adder and Multiplier" by Evor S. Vattuone, filed Aug. 21, 1974 and assigned to the present assignee. Although this implementation is capable of producing good results, it has certain drawbacks. The hardware design is highly dependent on the parameters of the particular radar simulated, and is further complicated for multimode radars having multiple PRF's and scan rates. In addition, the material cost can rise prohibitively should the radar have a wide beamwidth or a high PRF and low scan rate.